How do I bend a Model with an Armature? (Worm, Caterpillar, Tentacle...)
I'm not sure it will fit your need because it looks like your object is stiff and my solution is rather for a flexible caterpillar/tentacle kind of object. Anyway here is a solution with the Spline IK constraint. Contrary to other methods, you can easily stretch and twist your object in all the directions. Nota Bene: You should use several layers to make it easier to prepare:


Create a 5 bone armature (2 short, 2 long, one short), the first one will be the root, make the 4 other bones as long as the mesh.





Disable the Deform option of the root bone, it won't have any weight on the mesh.





Create a curve as long as the 4 front bones, subdivide it and make the vertices overlay the bones head.





Give the front bone a Spline IK constraint, choose the curve as Target, give it a Chain Length of 4.





As you can see, your curve vertices now control the bones head.





Switch your armature to Pose mode, select the root bone, then select the curve, shift select the bone, and parent with a ctrlP > Bone.





Now to make the control much easier and to be able to come back to a basic rest pose, you're going to create a second armature that will control the curve vertices: First create a bone for each head.





Switch this new armature to Pose mode, select a bone, now shift select the curve, go in Edit mode, select the corresponding vertices, and press ctrlH > Hook To Selected Object Bone. Same for all the other bones.





Now as you can see, the new armature control the curve vertices.





Switch the first armature to Pose mode, select the root bone, then select the second armature, select again the root bone and ctrlP > Bone. Now when you'll move the first armature it will move the whole thing.





Change the display of the first armature from Octohedral to B-Bone, Segment the 4 front bones (2 or 3 segments) to have a more flexible armature. Don't do it if you want to keep a stiff object.





Parent the mesh to the first armature with a ctrlP > With Automatic Weight.





Make sure that the Armature modifier is above the Subsurf. Enable the Preserve Volume option.





It should work.